Equivalences of the large deviation principle for Gibbs measures and critical balance in the Ising model

In this paper we obtain the equivalence of the large deviation principle for Gibbs measures with and without an external field. For the Ising model, the equivalence allows us to study the result of competing influences of a positive external field h and a negative boundary condition in the cube λ(B/h) as h searrow 0 for various B. We find a critical balance at a value B0 of B